The 9/11 Forum

Connectors must be weaker than the card floors, for sure, and not be able to transmit any bending.

It can be done to weaken the card - cut half through it with a knife - adjacent to the Lego wall.

David B. Benson wrote:OneWhiteEye --- Other possible connectors are

cut paper matches --- maybe cut in half, length wise
cut wooden match sticks --- maybe sliced into quarters, lengthwise
cut toothpicks

Any of those ought to provide a more uniform collection of connectors, methinks.

Yes. Plastic straws, sipper straws, too. I haven't gone digging in my buckets of Legos yet for an inventory; I may propose an equivalent wall material should the parts be unavailable.

Heiwa wrote:Hm, it's not good, is it?

No, probably why toilet paper is not the best choice for an interesting experiment here. Still, the likely results are noted, similar to that of floors of air.

David B. Benson wrote:OneWhiteEye --- I think having all the "floors" the same size is important. While I don't think it will happen, the model is to admit at least the possiblity of early crush-up, which means the lower cards need to fit up inside zone C.

Here's a side-view schematic of upper and lower wall section, do I have the idea?

The real connector cannot transmit any bending moment to the wall!

Upper part C must collide with the floor and the floor must then do its job: either transmit the force to the wall as shear ... or get crushed.

OneWhiteEye --- Yes, that is what I had in mind.

The model now suggests that the walls of upper part C contacts the connector of part A, i.e. no floor contacts any floor.
Upper part C must then be horizontal so that contacts on the connectors take place simultanesously. Anyway, I have a feeling upper part C will ge jammed inside part A pretty soon in this model.

Heiwa wrote:The real connector cannot transmit any bending moment to the wall!

Good point. Ideally, the wall is so strong that it will not react to the moment.

The model now suggests that the walls of upper part C contacts the connector of part A, i.e. no floor contacts any floor.

Like this?



A concern of mine, too. It seems the experiment is tipped towards crush down. This is part of the reason for my earlier confusion, where I thought this was a demonstration of crush-down progressive collapse, with an attendant chance of upper block failure if the hat truss is too weak. In order for it to demonstrate that crush-down occurs instead of crush-up when both are equally likely, there has to be a chance that crush up will occur in a situation that favors it. To obtain such a situation, may I suggest two variations:

1) Drop the upper block from the same height, but with no block below it. Let it strike the tabletop; does crush up occur?

2) Take the same entire assembly and invert it, such that the lower block is now the upper block. Assume the floors have been tacked to the connectors so they don't fall when everything's upside down. Drop the (formerly lower, now upper) block, which still fits around the outside perimeter. Does crush down occur, or does the bottom block knife its way through the top?

The model should not be constructed in a way that favors one or the other unless the express purpose of the model is to show that the geometry involved in the collapse prevents crush-up from occurring. I can see how an upper block which wedges inside the lower creates an asymmetrical situation favoring the shearing of lower floor connections - something which this model does demonstrate. So, I can't say the model does not deliver on what it purports because I think it does. I'm just wondering if there isn't a way to go that extra distance to show that crush-down is favored when both are possible - favored because the upper is a free body.

Due to the contact region being composed of the the Zone C lower wall and Zone A upper floor connectors, we see a situation where equal and opposite impulse is directed into two very dissimilar components. For Zone A, the impulse will act on the eight top connectors, and some portion (total minus connector deformation) will be transmitted to the rest of the structure, whereas the impulse on Zone C will be effectively transmitted to the entire Zone C structure. Naturally, the same force on a much greater rigid mass will necessarily produce a much smaller velocity change in that body, possibly so small it won't even jar the floors upper floors much even if they aren't tacked.

While it is true the geometry permits the lower floors to go up into Zone C, there's no force that will put them there. After shearing (or pullout/bending) of the connections, there's nowhere for them to go but down, as both Zone C rigid walls and gravity provide downward directed force. Again, that might be the point.

Anyway, I have a feeling upper part C will ge jammed inside part A pretty soon in this model.

Connector sizes exaggerated for clarity, but you may still be right.

It seems your model is just about a wall (perimeter columns) of an upper part C contacting a connector fitted in the wall of a lower part A. OK, we start with the details.

I would assume the connector is simply sheared/cut off by the upper part C. It requires energy E provided by gravity that you can calculate, e.g. the cutting force F involved (you must calculate that one) and the distance d this force ploughs throw the connector to complete the job. E = F d.

Don't forget Newton, e.g. the connector applies a force on part C that will try to stop part C cutting the connector. Self defence. The connector might not succed but I assure you that part C will be slowed down.

I have never managed to cut connectors letting gravity do the job (just dropping something on it).

OneWhiteEye wrote:1) Drop the upper block from the same height, but with no block below it. Let it strike the tabletop; does crush up occur?

I don't think this matters.

2) Take the same entire assembly and invert it, such that the lower block is now the upper block. Assume the floors have been tacked to the connectors so they don't fall when everything's upside down. Drop the (formerly lower, now upper) block, which still fits around the outside perimeter. Does crush down occur, or does the bottom block knife its way through the top?

Excellent idea. I'd just change this by building another such demonstrator with the floors untacked resting on the tops of connectors.

The model should not be constructed in a way that favors one or the other unless the express purpose of the model is to show that the geometry involved in the collapse prevents crush-up from occurring. I can see how an upper block which wedges inside the lower creates an asymmetrical situation favoring the shearing of lower floor connections - something which this model does demonstrate. So, I can't say the model does not deliver on what it purports because I think it does. I'm just wondering if there isn't a way to go that extra distance to show that crush-down is favored when both are possible - favored because the upper is a free body.

Yes.

While it is true the geometry permits the lower floors to go up into Zone C, there's no force that will put them there.

Not quite, but close enough. That's what Bazant & Le show.

The goal is to design the spacing between the walls and the connectors in such a way that no jamup occurrs. Ideally the connectors shear off, but if only bent there has to be enough clearance so that friction does not prematurely terminate the experiment.

David B. Benson wrote:I don't think this matters.

All depends on the criteria. I'm sure you agree that, while the floors might drop out on impact, there will be nothing crushing up in this scenario. This indicates that, as intuition suggests, it is impossible for crush-up to occur in this model unless something is able to drive upwards into a Zone C block. The tabletop, being a flat and rigid surface, cannot provide any geometry to thrust up and break floor connections above its level. I claim the floor slab and connectors of Zone A, while yielding and non-rigid, present essentially the functional equivalent of a tabletop - a flat plane from which nothing can project upward.

There are not so subtle alterations that could change the results dramatically. One is my other suggestion to invert the contraption; this is simply swapping architectures between upper and lower. The equivalent is make the lower block go inside the upper. Here, I'd expect exclusive crush-up. That which fits inside the other is the hole-cutter in this scenario. The model is not invariant to geometric substitutions. If my understanding is correct, the model can be used to demonstrate either crush direction, according to how it's built.

Of course, if indeed the upper block of WTC1 did shimmy down inside the lower walls, this model should correspond to an actual mode of collapse - shearing of connections with a plug being forced downward by mass above. The model is worthwhile. I'm about to inventory Lego bricks, but first...

I'll speak for myself, but I believe these questions about the nature of crush-down/up dynamics are fairly widespread. The Bazant et al series of formulations embrace a 1D, essentially homogenous model of structure and dynamics. While it is acknowledged that this model is a necessary simplification, it is also claimed the assumptions of the model portray a scenario most favorable to survival and that the result is sufficiently accurate to show the model properly captures the dynamics. Thus, there is no need to consider tilt except as a correction to actual displacement measurements, no need to invoke shearing of floor connections or wedging, or any of that; the solution of the equations of motion show the structure is capable of buckling all vertical members, crushing the contents and concrete, etc. Bazant, in his reply to Jones, even put forth an apparently sound argument for why almost no crush-up is expected until crush-down has completed, a subject being discussed now in a different thread.

Why then the difficulty visualizing an actual process which satisfies these characteristics? If the science is sound, everyone should be on board. Our everday experience says that like-impacting-like produces like damage. Granted, (e.g.) vehicle collisions are between two bodies subject to the same external forces. Two Pintos colliding in reverse at 90 mph should both burst into flames. An upper block falling on a lower is a free body impacting another similar, though larger, body which is fixed under its own structural integrity. Free and fixed. That's the only difference and, somehow, it needs to make a world of difference. I'm not surprised when people have a hard time accepting that the difference is: if you stack 9 Pintos atop each other, and drop a 10th on the stack, it crushes its way to the bottom before experiencing any significant damage to itself. That's clearly insanity, but it's not really an appropriate model.

Where's the disconnect, and what can be done to bridge the gap? Does it matter if the autos are made of glass instead of steel? Or if the top car is dropped from a height of a kilometer? Or if the experiment is conducted in a centrifuge?

What would help is to be able to demonstrate these very same principles on an everyday scale. Perhaps this is not possible. Maybe everyday materials at tabletop scales cannot exhibit this behavior. Thin steel structures in excess of 400m tall may simply be out of the realm of constructions that can sit on my table. Here, I think the theory should be consulted for guidance. For once, can we put values into these equations which represent two of mass, length, or DCR (of something other than a tower) and solve for the third under conditions of collapse completion? Surely this theory is amenable to tabletop dynamics as well; if it isn't, my first and last question is why.

The tabletop model here is useful. I'm not trying to blow it off in any way. Rather, I'm attempting to get at the meat of what has been a stumbling block for apparently very many otherwise intelligent people. How does a structure, which is well modeled as a 1D homogenous structure, give a solution which dictates the upper, smaller portion survives through the destruction of the larger lower? Ultimately, this question can't be answered to any degree of satisfaction by a model which requires a 'stacked deck' to achieve this end. Even if the model more closely approximates the real collapse scenario than do the scientific articles, the articles stand firmly on a foundation which does not require all the messiness and geometry of the real collapse.

I accept that rubble alone can crush down what's below it - but rubble is that which has already been destroyed! Just because it's not at its original elevation or higher does not mean it was crushed down. Things break and they fall down, when in a gravitational field. Bazant has declared the rigid, yes FULLY intact, upper block is not merely a simplifying assumption but dictated by the dynamics. At least on axial impact... OK, so there wasn't axial impact, but can we test his theory, too, while we're at it?

What would impress me is a physical model in which one could assemble two identical blocks, choose at random which is to be upper and lower, then drop one on the other and watch ONLY the bottom one be destroyed. This does not even account for a smaller, weaker block doing the damage, so some might not be satisified with it - but it's a step. Note that I impose no strength requirement other than that which is required for one block to be able to stand under its own weight. The lower structure could be incapable of statically supporting a similar upper structure. In some respects, this might be better, because what we'd then expect to see is a quasi-static initiation, more like the towers, and a collapse that should be guaranteed to go to completion.

A suitable alternative is to use the theoretical framework to show why it's not possible to do this on a desktop.

OneWhiteEye wrote:The equivalent is make the lower block go inside the upper. Here, I'd expect exclusive crush-up.

Nope. No (significant) early crush-up.

And that is all that this sort of demonstrator is intended to show.

Or if the experiment is conducted in a centrifuge?

That will make a substantial difference.

What would impress me is a physical model in which one could assemble two identical blocks, choose at random which is to be upper and lower, then drop one on the other and watch ONLY the bottom one be destroyed.

Well, these Lego bricks and playing card models are not exactly identical, but choose at random whether the wider one goes on top or bottom. That is as close as we are likely to be able to get without some seriously difficult model construction.

David B. Benson wrote:

OneWhiteEye wrote:The equivalent is make the lower block go inside the upper. Here, I'd expect exclusive crush-up.

Nope. No (significant) early crush-up.

And that is all that this sort of demonstrator is intended to show.

Ah, then, it makes the experiment all the more interesting, because I believe it will go the other way. Beware experimenter bias !! haha

Seriously, I have to make sure we're on the same page and that the apparent disagreement is not a matter of definitions. If the lower block is instead the narrow one, you expect there to be crush-down only. Does this mean shearing of upper block floor connections with concurrent (or leading) floor failures (pancaking) going down into the lower block? Because I'm pretty sure it doesn't mean vertical buckling of the Lego walls due to contact with the floor connectors!

See, I don't know about that; it's borderline. In order for upper block floors to penetrate the interior of the lower block, they must first be severed from the upper block. True, if the connections were weak enough, dropping one slab onto another could initiate pancaking which is a limited case of crush-down. But then we could simplify the model further and use only a single floor slab to produce the same result.

A more interesting case is where it takes a multiplicity of floors to overload a single floor's connectors. Here, the situation will go to interior pancaking after enough floors have been sheared from above, but the pancaking system at that point becomes physically decoupled from the rest of the model, i.e., would continue if the remaining upper block were stopped artificially at that time.

In these cases, I would define the system as experiencing crush-up until debris can cause pancaking. I take it your definition is not the same?

OneWhiteEye --- You are right and I am wrong. This is a connector controlled crush-down demonstrator.

OK! No problem. As an aside, I went to the storage area to see what Legos I had on hand. Whoa. I don't know what made me think they were all together. Buckets and baskets of undifferentiated toy junk. There are probably quite a few pieces mixed in with all that stuff, but the entropy is overwhelming! So it's probably a good thing that it's back to the drawing board, in some respects.

Let's see what we can come up with. First, let me ask this: do you accept simulation, however crude, if carefully done and well-characterized? I can build a lot more with a keyboard than with a coping saw and glue gun.